(3x-7)(4x-5)+x=5

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Solution for (3x-7)(4x-5)+x=5 equation: 


Simplifying
(3x + -7)(4x + -5) + x = 5

Reorder the terms:
(-7 + 3x)(4x + -5) + x = 5

Reorder the terms:
(-7 + 3x)(-5 + 4x) + x = 5

Multiply (-7 + 3x) * (-5 + 4x)
(-7(-5 + 4x) + 3x * (-5 + 4x)) + x = 5
((-5 * -7 + 4x * -7) + 3x * (-5 + 4x)) + x = 5
((35 + -28x) + 3x * (-5 + 4x)) + x = 5
(35 + -28x + (-5 * 3x + 4x * 3x)) + x = 5
(35 + -28x + (-15x + 12x2)) + x = 5

Combine like terms: -28x + -15x = -43x
(35 + -43x + 12x2) + x = 5

Reorder the terms:
35 + -43x + x + 12x2 = 5

Combine like terms: -43x + x = -42x
35 + -42x + 12x2 = 5

Solving
35 + -42x + 12x2 = 5

Solving for variable 'x'.

Reorder the terms:
35 + -5 + -42x + 12x2 = 5 + -5

Combine like terms: 35 + -5 = 30
30 + -42x + 12x2 = 5 + -5

Combine like terms: 5 + -5 = 0
30 + -42x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(5 + -7x + 2x2) = 0

Factor a trinomial.
6((1 + -1x)(5 + -2x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1

Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {1, 2.5}

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